SSC & BANK EXAMS: REASONING · INEQUALITIES

Inequalities (direct and coded)

Two letters are related only if every sign between them points the same way. Any > or < makes it strict; only = signs give equality.

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Worked examples

Example 1 · level 1

Statement: R < U ≤ V. Which of the following is definitely true?

U = V
R = V
R < V
U < V

Show solution

Chain: R < U ≤ V.
Between R and V: <, ≤: all in the same direction, with a strict sign.
So R < V.
Every other option either has opposite signs on the way or claims more than the chain gives.

Answer: R < V

Example 2 · level 2

‘A $ B’ means A is greater than B; ‘A @ B’ means A is greater than or equal to B; ‘A # B’ means A is equal to B; ‘A ★ B’ means A is smaller than B; ‘A & B’ means A is smaller than or equal to B. Statement: Q # T, T @ M, M # P. Which of the following is definitely true?

Q ★ P
T & M
Q # P
Q @ M

Show solution

Chain: Q = T ≥ M = P.
Between Q and M: =, ≥: all in the same direction.
So Q ≥ M, written as Q @ M.
Every other option either has opposite signs on the way or claims more than the chain gives.

Answer: Q @ M

Example 3 · level 3

‘A & B’ means A is greater than B; ‘A @ B’ means A is greater than or equal to B; ‘A ★ B’ means A is equal to B; ‘A # B’ means A is smaller than B; ‘A $ B’ means A is smaller than or equal to B. Statement: T # K, K # V, V & W, W # Q. Which of the following is definitely true?

T ★ Q
T # V
K $ W
K ★ V

Show solution

Chain: T < K < V > W < Q.
Between T and V: <, <: all in the same direction, with a strict sign.
So T < V, written as T # V.
Every other option either has opposite signs on the way or claims more than the chain gives.

Answer: T # V